Can I adjust bones after skinning and weight painting?
You can edit the armature as much as you like as long as the bone names remain the same.

You see, weight data is stored in the object in the form of Vertex Groups. Vertex Groups are a multi-purpose way of defining weighted areas in mesh that's used for all kind of things, skin weighting being one. The armature modifier just takes the incoming bone names and matches them with the names of the Vertex Groups. It's super flexible.

It's possible to even delete the rigify generated rig, do the adjustments in the metarig and generate a new one, and the armature modifier is like nothing happened.

The trick is to add the armature modifier without adjusting the pre-existing weights. Through parenting, you just have to choose "Armature Deform"



Or by setting the armature object in the armature modifier manually.



Both will leave your skin weight data as it was. No need to redo.

If the bone names have changed, for whatever reason, you only need to rename the corresponding Vertex Group to match the new one.